We warn the reader that \(A^\circ \)  need not be tfp over \(\mathcal {O}_K\)  even when \(A\)  is reduced; this pathology does not occur if either \(K\)  is discrete, or if \(K\)  is stable field with \(|K^*|\)  divisible (if \(K\)  is algebraically closed); see [1]} for the definition of stability, and [1]} for the finiteness properties.
